# Scale Drawing

### Task 41 ... Years 2 - 7

#### Summary

A shape is drawn on one grid and students are asked to redraw it on a grid with a different scale. They are practising several measurement skills in a non-threatening environment. Using the pen on the laminated board means mistakes are easily erased. Soon students become confident with the process and are able to draw a more permanent copy on graph paper.

Note: The laminated board (top right) was omitted from all eTask Packs purchased before the end of December 2019. Save and print from here and include with your other files.

#### Content

• location in 2d space
• recognition and counting units of measure
• drawing to scale
• length and area measurement
• informal experience with ratio
• introduction to similarity

#### Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

• Choose any length on the original and the corresponding length on the copy - even a sloping length. Measure these lengths using the same unit (eg: in centimetres). How do they relate?
• Measure the space inside the original and the space inside the drawing using the same unit (eg: centimetre squares). How do they relate?
• How do the angles in the your drawing relate to those in the original?
• What do you think of this statement from a Year 8 student: No matter how big the drawing gets the angles always stay the same?
• Design your own simple drawing on a large grid for someone else to copy on a smaller grid.
• What happens if we use different rules for copying horizontal and vertical lengths? For example, for each horizontal length on the original use one on the copy. But for each vertical length on the original use two on the copy.
• What happens if we make the copy on triangle line paper (equilateral triangles)? There are three directions on this paper. Choose one to be the 'horizontal' and one to be the 'vertical'. Ignore the other direction.
• Try the Freewheelin' Franklin Challenge.
(This character was created by Roland Seidel when teaching at Elwood High School. He was encouraging kids to learn to work like a mathematician long before Working Mathematically was the accepted core of mathematics education.)
You can also find scale relationships in Task 166, Sphinx.

#### Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

Use 1cm square line paper and the file designed for the laminated board in the task. Use the challenges on the card and in the Iceberg above to guide the initial lesson.

Prepare some 2cm grids printed on stiffish card and invite students to create their own scale drawing challenge and record it on these grids. Creations are first designed on graph paper before being recorded on the card. They can be buildings, vehicles, animal caricatures or anything else, but keep them simple. Collect and laminate the drawings.

When you have 15 laminated drawings they make a class set. Give one to each pair with a sheet of 1cm graph paper and ask them to reproduce the drawing using one length on the graph paper to match one on the original drawing. Are the two drawings the same size? Explore and explain. One key element is that the unit of length on the original drawing is not the same as the unit of length on the paper drawing, but they are connected. One unit on the original equals two on the paper drawing. This is the scale.

Original : Copy = 1 : 2
On some maps (especially Army Survey maps) you find scale statements like 1:1000 or 1:10,000. What could these mean? Suppose the original grids for the students' laminated drawings had been 3cm squares, how would the scale be written?
• Compare the areas inside the two drawings using the same unit. What do the students discover?
• Make a class display of the ways scale drawing is used in the world.
What happens if we don't use the same rule for vertical and horizontal lengths when copying the original drawing?

At this stage Scale Drawing does not have a matching lesson on Maths300.

#### Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

The Scale Drawing task is an integral part of:

• MWA Chance & Measurement Years 5 & 6